Dissolve or disintegrate part of mesh while it is animating?
I think you are looking for the Build modifier.

The build modifier erases your mesh, then animates it being "re-built" face-by-face.  Just add a Build modifier to your object, set the Start frame and frame Duration to the desired amounts.  Then check Reversed to have it progressively take away geometry instead of building it from empty.



To get a more dissolve-like effect I would also check Randomize, this makes it randomly choose faces to take away, instead of sequentially doing connected adjacent faces.  Here is a side by side comparison, with Randomize checked on the left and unchecked on the right.